Yeah I'd say alot of what's been suggested is likely, Varenes may have been the final nail but Louis had been in trouble for a while by this point. Irony of Ironies his best hope at this point was to get away with the flight, reach Royalist or Austrian forces and clear off into exile. If the royal's escape they become a rallying point for the royalist forces, if they hang around then sooner or later the radicals would find a reason to kill them.
However without the flight there is less of a ready made excuse to begin the process of setting up the republic since the event that scuttles the King's popularity totally hasn't happened. That could lead to problems with the mob later on if their loyalty to the King isn't totally broken as it was after his betrayal by trying to reach the Austrians in OTL. This might give the moderates more support but I think the terror was coming sooner or later...
However the republic had deep problem's from the start, and Napoleon or someone like him may have been inevitable. If the result had been a moderate US style Republic that stayed in it's European borders and tried to get on with other nations it might have been allowed to survive. Once you get a radical expansionist state desiring to throw over all the previous European powers, well the reactionary forces only choice was to crush it and make sure it stayed crushed...